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Preliminary and to be Completed
Last Updated Jan-12-2011
Abstract
We present a concise quantitative method for combining value and
momentum strategies in a tactical asset allocation framework by directly
comparing the attractiveness of valuations across a broad range of asset classes.
Our broad and diverse publicly traded asset classes include public equity,
investment grade and high yield bonds, cash, Treasury Inflation Protected
Securities (TIPS), commodity and real estate. We refine the basic yield
approach to valuation by standardizing the value signal using the Z-score. By
tactically adjusting the weight of each asset class based on its perceived value
and momentum signals, our model shows significant improvement in overall
portfolio performance.

Introduction
Clifford S. Asness et al. have documented in their 2008 paper “Value and
Momentum Everywhere” that value and momentum deliver abnormal positive
expected returns in a variety of markets and asset classes at the security level
(Asness, Moskowitz, & Pedersen). The key issue we address here is whether
such effect can also be observed across asset classes at the index level in a
tactical asset allocation framework. More specifically, we want to examine

whether we can improve on a given strategic asset allocation by tactically
adjusting the weights of asset classes based on their perceived value and
momentum attractiveness. The strategic asset allocation here is a
representative mix of a broad and diversified seven (7) asset classes, including
world equity, investment grade bond, high yield bond, cash, TIPS, commodity
and real estate. For practitioners, our model provides a dynamic top-down
approach to tactical asset allocation in accordance with the ever-changing
market environments.

Data and Methodology
Table 1 is an overview of the seven asset classes that set up the framework
for our analyses and the indices that we used to measure the value and
momentum signals. The selection of the asset classes is not based on a formal
set of rules. In fact, each asset class should provide a unique set of return and
risk characteristics so that a portfolio of the asset classes would provide
diversification and reduce the overall risk. More specifically, investments
should provide growth as well as protection against both deflation and inflation
risks most institutional investors face. Existing literature suggests that high yield,
commodities and real estate add most value to the traditional asset mix of
stocks, bonds and cash (Mars, Robeco, & Rabobank, Ocotober 2009). Equity
would provide growth and include both U.S and non-U.S. equity, as the
distinction between the two has lost some of its meaning over time. Fixed
income performs better than equity in a deflationary or weak economic
environment and is a portfolio of the three unique return/risk characteristics
for the asset class –investment grade (yield curve risk), high yield (credit risk)
and cash (no risk). Inflation-hedging or real assets include a basket of assets
3

The indices that we use to represent our seven asset classes are (table 1):
the Morgan Stanley Capital International ACWI Index (MSCI ACWI), Barclays
Capital Aggregate Bond Index (Barclays Agg.) gross return, Merrill Lynch High
Yield Master II (MLHY II) total return, Merrill Lynch 91-Day Treasury (Cash),
10 year on the run Treasury Inflation-Protected Securities (TIPS), Goldman
Sachs Commodity Index (GSCI) total return, and National Association of Real
Estate Investment Trusts Index (NAREIT) global total return.
It is comparatively easy to apply momentum strategy to cross-asset
allocation since it only requires past prices as inputs. We use the return based
on last month price over a simple moving average (SMA) of trailing 12-month-
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ending prices
2
for the momentum signal. We consider such momentum signal
negative if the return is negative. The SMA offers a smoothing mechanics on
the momentum signals. Previous study also shows that a trend-following SMA
model could increase risk-adjusted returns (Faber, Februrary 2009).
It is less straightforward to construct a cross-asset allocation value
strategy, because no obvious valuation measure is applicable to every asset class.
The starting point of our approach is a simple yield measure for each asset class
(Blitz & Van Vliet, 2008). We use the book-to-price (B/P) for equity assets,
cash-flow-to-price for REITs, and the standard yield-to-maturity for all the
bond assets, including investment grade, high-yield, cash and TIPS. For
commodity, we use a backwardation-contango measurement, defined by (next
month futures price - current month futures price)/next month futures price. If
such signal is negative, it is in contango; and vice versa, if it is positive, it is in
backwardation. Backwardation is a value situation because of the roll-yield. All
valuation data are from 1986 January
3
except TIPS from 1997 March. The
yields on T-Bill and TIPS are from Federal Reserve System; Cash-flow/Price
for NAREIT is based on Goldman Sachs respective US REIT universe
4
. The
backwardation/contango signal is calculated from GSCI generic futures prices
from Bloomberg.
All the above valuation measurements share the same feature that the
bigger the value, the more attractive the valuation. Obviously, it is less
meaningful to directly compare our basic yield measurement of equity (B/P) to
investment grade (yield), or the yield of investment grade to that of high yield.
In order to compare the value measurement meaningfully across asset classes

2 One can also use 10-month, 6-month, 3-month and so on. For simplicity we just use 12-month as an example.
3
Valuation data for emerging market started in Jan-86.
4
The use of NAV-to-price data based on UBS respective of US REIT universe will not change our conclusions.
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and account for the inherited structural difference, we refine our basic yield
approach by standardizing the value signal. We calculate the Z-score at any
given month t, using its entire historical data up to month t, based on the
following formula:
Z =
I
t
-mcon(I
0,t
)
StJ(I
0,t
)

Such Z-score, measuring how far the signal is away from its historical
mean in terms of how many standard deviations in between, offers a direct way
to compare the attractiveness of valuation of different asset classes and
provides insights to the allocation for month t+1.
It is also worth noting that for both value and momentum
measurements, we only use historical data up to any given time t, in order to
avoid forward-looking bias.

The Quantitative System
We analyze the performance based on two (2) sets of policy/base
weights. One is equal weighted. The other is a set of hypothetical weights,
which serves more conventionally to institutional investors. Since TIPS is not
introduced until early 1997, we have six (6) asset classes before March-1998 and
seven (7) asset classes including TIPS after
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. Table 2 provides an overview of
the two policy benchmark weights.

We first examine momentum and value strategy separately and then
combine them with trend-following model in the tactical allocation framework.

Momentum - At the end of every month, we rank our seven asset classes
based on their momentum signal. The ranking is used to adjust the asset class
weights from the policy or base weight. For asset class i, the momentum
suggested weights are:
w
m
(i) = Bosc(i) + R - (ronk(i) - o:crogc(ronk))
Where R is the adjusting basis, a parameter we can change. For now, we set R
= 2%, which will satisfy the fully-invested, no-leverage and no-short constraints
and result in very small deviations from the benchmarks. For the case of seven
asset classes, the average rank is equal to 4. In this way, the summation of the
weights will keep unchanged after the adjustment.

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Value – Following the same idea, each month we look at the value
measurements, i.e. the Z-scores, to identify any asset class that is significantly
under/over-valued and take advantage of the long-term mean-reversion
mechanism. Meantime, as an effort to avoid “value trap,” we only increase the
weight of the undervalued asset class with a Z-score above 2. Consistently, we
also only reduce exposure to the overvalued asset class with a Z-score below -2.
Please keep in mind that the bigger the Z-score, the more attractive the
valuation is. In other words, we identify any asset class whose valuation is at
least two-standard-deviation cheaper/more expensive than its historical mean.
The asset class with a Z score between -2 and 2 will be treated as 0. Just as
momentum strategy, we use ranking to adjust the asset class weights from the
policy weights. Asset classes with the same Z-score (0) will have the same rank.
w
¡
(i) = Bosc(i) + R - (ronk(i) - o:crogc(ronk))

We combine momentum and value strategy with the trend-following
model as shown in Exhibit 1.
Exhibit 1

Step 1 (Momentum): Each month, we first apply the momentum strategy to
calculate Wm.
Step 2 (Trend following - optional): We could then follow a simple trend
following the model developed by M.T. Faber (Faber, Februrary 2009). If any
Base
Momentum
W
m
Trend-
Following
W
mt
Value
W
mtv
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Instead, one can chose to only invest in undervalued (Z > 2) asset classes, but not reduce exposure to
overvalued ones; similarly this step will improve Sharpe ratio but reduce information ratio as it increases
tracking error.
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Preliminary Results and Robustness Test
The main results are presented in Table 3-5. E and H stand for the
equal-weighted and the hypothetical benchmark portfolios respectively. The
strategy applied to the benchmark portfolios is noted in the brackets. “V” and
“M” stands for the value strategy and the momentum strategy. “MT” means
combining momentum strategy with the trend following model. “M&V”
combines value and momentum without step 2, while “MT&V” includes both
step 2 and 3. An annual risk free rate of 4% is used for Sharpe Ratio analysis.
Testing period is from 1989 January
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to 2010 September.
We examined the robustness of our findings and computed alpha, beta
and T-stat for each strategy against its policy benchmark from monthly return
data. The monthly risk-free rate is downloaded from Fama/French website. We
also examine if step 2 and 3 in the combined model has generated alpha by
using intermediate results as benchmark, i.e. use M only as benchmark for MT
and MT as benchmark for MT&V.

Our model shows improved overall performance based on both
benchmark portfolios. Value and momentum alone will both generate
significant alpha
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. By nature, momentum strategy will adjust weights every
month. Meanwhile, value strategy was triggered 149 months out of the total
261 months test period with a critical Z score of two(2)
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. We also see that the
simple equal-weighted portfolio offers better diversification and risk-adjusted
return (higher Sharpe Ratio) than the more conventional equity heavy
allocation (the hypothetical portfolio) in the long run (Maillard, Roncalli, &
Teiletche, May 2009). The trend following mechanism (step 2) acts as hedging
by moving capital to cash, and improves the risk-adjusted return in the long run

10
For our sample, the critical value of t is about 1.65.
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Out of the 261 months, there are 149 months when one or more asset classes have a Z score less than -2 or
bigger than 2. This is also a parameter that can be changed. A smaller threshold will obviously
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because of capital preservation. The maximum drawdown is reduced by more
than 20% in our framework. However, momentum combined with trend
following may not do as well at market turns, e.g.2009. Further adding the
value strategy (step 3) could help to identify the opportunity to participate in
the market rally (see exhibit 2).

The effect of R can be demonstrated through a simple example. We look
at the 20-year Sharpe Ratio of the combined model on the equally-weighted
benchmark portfolio. As we increase R, we need to relax the no-short no-
leverage constraint and the Sharpe ratio is optimized around R = 7% with a
value of 1.18. Under the no-short constraint, the maximum value allowed for R
is about 4.76%, which gives a 20-year Sharpe ratio about 1.17
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.

Following the same methods, we still use the index data as inputs, but
use real ETF returns to calculate performances. We compare the model’s
performances with our benchmark index
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returns, ETF returns
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and sample
performances of about 200 foundations and endowments in the BNY Mellow
Trust Universes.

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JNK, in fact, tracks the price and yield performance of the Barclays Capital High Yield Very Liquid Index.
14
See table 1.
15
Since the inception of ACWI is 2008/04, the performances using all ETFs only have about 2 year track
record.
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We can see, even with a very small adjustment R=2%, our model
outperforms the top 25% in the pool in the long run using a return-only
judgment. The performance difference between the ETF and the index is in
general due to the tracking error, premium/discount to NAV and management
fee. Using ETFs, our model on equal-weighted benchmark still put itself close
to the top 25% in recent periods. Thus our model offers a low-cost and easily-
accessible way for individual investors to achieve institutional investor type
returns, without the complication of hedge fund and private equity type
managers that requires much more expertise and capital (Rittereiser & Kochard,
2010). In fact, hedge fund and private equity type managers need to
compensate investors much higher net returns for their illiquidity.
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We need to be careful about the liquidity constraint and the transaction
cost of our model. Some ETFs can be very illiquid and have high market
impact cost. However, with the fast growing popularity of ETFs, we may find
better, cheaper and more liquid ETFs to replace or add to the ones here for
each of the asset class to solve the issue.

Conclusion
Our strategy is basic by design, and the results are significant. Meanwhile,
further considerations and care must be taken on this instructive model before
implementation, such as liquidity constraint, transaction cost, tax and so on.
Several improvements can also be done. For example, we could seek to add the
benefit from active stock picking by using information from hedge fund’s 13F
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and 13D
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. Other indicators of market risk (Sullivan, Peterson, & Waltenbaugh,
2010) can also be tested for market-timing.
Bibliography

16
Required by SEC, hedge funds need to report their quarter ending long positions within 45 days.
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The form is required when a person or group acquires more than 5% of any class of a company's shares.
This information must be disclosed within 10 days of the transaction.
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